By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit c...By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.展开更多
In this paper,we present local discontinuous Galerkin methods(LDG)to simulate an important application of the 2D stationary Schrödinger equation called quantum transport phenomena on a typical quantum directional...In this paper,we present local discontinuous Galerkin methods(LDG)to simulate an important application of the 2D stationary Schrödinger equation called quantum transport phenomena on a typical quantum directional coupler,which frequency change mainly reflects in y-direction.We present the minimal dissipation LDG(MD-LDG)method with polynomial basis functions for the 2D stationary Schrödinger equation which can describe quantum transport phenomena.We also give the MDLDG method with polynomial basis functions in x-direction and exponential basis functions in y-direction for the 2D stationary Schrödinger equation to reduce the computational cost.The numerical results are shown to demonstrate the accuracy and capability of these methods.展开更多
文摘By using the extended F-expansion method, the exact solutions,including periodic wave solutions expressed by Jacobi elliptic functions, for (2+1)-dimensional nonlinear Schrdinger equation are derived. In the limit cases, the solitary wave solutions and the other type of traveling wave solutions for the system are obtained.
基金supported by NSFC grant No.11031007,FANEDD No.200916,NCET No.09-0922Fok Ying Tung Education Foundation No.131003.
文摘In this paper,we present local discontinuous Galerkin methods(LDG)to simulate an important application of the 2D stationary Schrödinger equation called quantum transport phenomena on a typical quantum directional coupler,which frequency change mainly reflects in y-direction.We present the minimal dissipation LDG(MD-LDG)method with polynomial basis functions for the 2D stationary Schrödinger equation which can describe quantum transport phenomena.We also give the MDLDG method with polynomial basis functions in x-direction and exponential basis functions in y-direction for the 2D stationary Schrödinger equation to reduce the computational cost.The numerical results are shown to demonstrate the accuracy and capability of these methods.
